Tag Archives: meter

I’ve just added Roger Grant’s Beating Time and Measuring Music in the Early Modern Era as my top choice for books on music theory for those interested in music-dance relationships (see my metre and rhythm page for a brief bibliography on that topic). I don’t want to say too much, because it figures largely in a chapter in my PhD, and it’s too detailed and scholarly a book for me to summarize hastily. Suffice it to say, if you want to know what I think about time signature and meter and movement, it’s all in this book. I’m glad I hadn’t read it when I was writing How Down is a Downbeat?, a journal article on music, ballet teaching and time signature that I wrote a few years ago; it would have tempted me to rewrite the whole thing. On the other hand, I wish I had read it when I first started teaching music for dance teachers back in 2000. However, some of the significant books and articles that Grant refers to in building his theory were published some years later than that. Is theory even the right word? I’m not sure: it’s history, but in order to understand the history, you have to change your ideas about what you thought was music theory. It’s amazing that in the 21st century, we’re still solving the problems unexamined or hidden by “rudimentary” music theory, e.g.—to name but one— why is a 6/8 called a compound time signature? What’s compound about it?

The biggest problem with what is conventionally called “music theory” is that it presents as simple and straightforward (a matter of counting two or three) something which is exasperating in its complexity, not least because “time signature” as a subject leaves out the people who use it and the way they interpret it, but it is virtually meaningless without the (changing) practice in which it is embedded. I’ve hinted at this in many of my more recent postings on triple meter and Rothstein’s theory of “Franco-Italian hypermeter.” Grant discussed the way that the meaning of beat as movement has gradually disappeared, morphing into the concept of time as a endless stream of motionless, durationless ticks. This in fact was exactly how I used to teach music theory and meter, without realising the entailments or history of my own beliefs about what meter or musical time was.

I am in awe of the way that Grant makes sense of such a complex assemblage of notation, musicians, practice, ideas, primers, teachers, and so on. It’s only when you’ve struggled to sort out some of these problems yourself that you realise how courageous and hard-working someone else has been at grappling with similar issues.

A proud day for me, my first proper article published in Empirical Musicology Review. “How Down is a Downbeat? Feeling Meter and Gravity in Music and Dance?” came out of a single teaching session, when about 12 years of trying to teach about meter and time signature finally imploded in a discussion with students. For people who wonder why I’m doing a PhD, and what I’m writing about, this will give you an idea – not of the subject, but of the problem.

It would be nice to think that perhaps this might open up a conversation about the musical components of dance teaching courses, but I somehow doubt it will – and for as long as that’s the case, I guess dance teachers will keep saying “By the way, I don’t do time signatures,” and be perfectly justified in doing so, in my view.

I’m still hopelessly behind with the 52 cards, which is annoying me, but I’ve not given up yet.

You can never have enough grand allegro, and this is handy because it’s in a class of pieces that are ballet music, which means that you have to be careful where you play them, but on the other hand, it’s repertoire that’s not often performed, so either people won’t know where it’s from, or they’ll smile and go “Isn’t that…??” and you look good because you know weird stuff that you found on Youtube. The solo is at 48’46” in the clip below. It should start there automatically when you click, but if it doesn’t, drag the slider to the correct time.

See also:

Sheet music for Drigo’s Diane and Acteon pas de deux from Esmeralda, with that fabulous coda, and gutsy male solo, from one of the best ballet music sites on the internet. This is one of the most confusing things in the world of ballet music, since to gala-goers, Diane and Acteon and Esmeralda have nothing to do with each other.

Esmeralda male variation music: the meter (for geeks only)

This should reallybe in the Clubs suit, not Hearts, because it’s actually a truly triple meter, not the dodgy six-eight kind—the phrases end on the eighth count, not the seventh. What fooled me was the melodic phrasing, which is in two bar units, which definitely feels duple. But look more closely, and not only are the cadences on 8, but also the harmony changes every bar, which strengthens the case for truly triple metre even more. Also, the introductory vamp before the first jump is one bar long, not two, which aligns somewhat with what William Rothstein has to say about “Franco-Italian hypermeter.” I transcribed this from the recording, so I don’t know whether in fact Drigo did write in 6/8, in which case the single count vamp would align with that theory even more. If it were the case, then the “extra” bar in the middle is not extra at all, because the melody begins on the half-bar in a 6/8 (but don’t try actually playing it that way in class).

On the other hand, it could just be a kind of compositional economy: given that you’ve already got an eight-bar phrase of entrance music, you don’t want to prolong the vamp any more than absolutely necessary, so keep it short, if you must have one. Maybe it’s there to provide the dancer with a run-up into the first jump (the vamp-like nature of the music telling the audience that what’s happening isn’t yet dance, just preamble to be ignored.

Once you start thinking about Rothstein’s theory (see other posts here and here) it makes something apparently as unimportant as an introduction suddenly fascinating, and it opens up all kinds of possible discussions about metre, grouping, phrasing, accent, and so on. For me, dance makes those questions particularly obvious because you’re dealing with accents and trajectories that happen in time, but they aren’t “musical” in the sense of being tied to time signature or accent. It’s like seeing a landscape compared to an ordnance survey map.

I was tempted to put the ballet-class equivalent of the Holy Family on the 25th of this advent calendar, to finish off the series with a heart-warming sentimental twist that starts “… in spite of all these things that make me anxious, I love playing for ballet, and these little things are what makes it exciting and interesting.” But just in time to save you from such a sugary end, I remembered the 9/8. This list of anxieties wouldn’t have been complete without it.

Now I’m not talking about the kind of 9/8 that’s just a 3/4 in disguise, that is, a tune that’s in three with a lot of “diddly diddly diddly” underneath it (see earlier post). I mean a proper 9/8 where the tune itself goes diddly diddly diddly diddly diddly diddly, without stopping for breath. I mean those 9/8s that are weird in the same way that the polonaise is weird, where phrases finish on the weakest possible (final) beat; where the end of the phrase feels like you’ve leapt on to the tube as the doors were closing, and just managed to pull your coat free as you got inside. Look at the example above – what kind of music ends on a little note like that? That’s like finishing a sentence with a comma,

I never trust myself to improvise them, because I have so often got hopelessly lost in the middle of them in class. It goes so well for so long, but it only needs one beat to go wrong to mess the whole class up, and once you’ve slipped up in a slip jig (another name for the 9/8), it’s hard to pick yourself up again. I’ve got a few in my head that I keep for special occasions, and stick to what I know.

It’s a strange pocket of ballet behaviour, the 9/8. It’s relatively rare in music*, but it seems someone once thought that it would be a good thing if ballet teachers learned about it, like you’d learn about the two-toed sloth, or photosynthesis. So the 9/8 crops up occasionally in class like a trick question, just when you least want or expect it. I rather like them, but they make me nervous.

Happy Christmas.

*Justin London wrote a paper called “The Binary Bias of Metric Subdivision and the Relative Complexity of Various Meters, or, Why is 9/8 so Rare?” given at the 4th International Conference on Music Perception and Cognition, Montreal, Quebec, August 1996. The background to the theory is also explained in his book Hearing in Time(second edition) on pp. 44-45.

In the course of writing an article about the problems of ballet and time signature recently, I read a lot of books and articles about 18th century theories of meter. I’ve already blogged about that several times recently, as I found a lot of it helped to answer queries I’ve had for years.

As the dust has settled on the thoughts that I had for the article, I have come to a conclusion, for now at least, that “mixed meter” as the 18th century theorist Koch used that term, offers a really useful way of understanding meter and time signature problems in ballet teaching. I began to formulate that idea in And now for something completely sextuple, but I could say it even more simply now.

The problems I’m talking about are almost exclusively to do with triple meter, and the fact that in the kind of music that you get in ballet classes (i.e. predominantly 8-count or 8-bar phrases) there is always a possibility of counting in 2 or 4 rather than 3 – and if trainee ballet teachers have to learn about time signature, they often have difficulty understanding why something should be classified as a 3 or a 6 when it seems more natural to count it in 4.

If Koch were to come back to earth and teach such courses, he probably wouldn’t say “you’re wrong, it’s a 6,” he would have said “this is a tripled 2,” or “mixed meter” – you’re right, it is four, because the tune is moving predominantly in a 1,2, 1,2, fashion, rather than diddeley diddeley diddely diddely style, like a double jig, or Schumann’s Der wilde Reiter/The Wild Horseman. Koch’s point was that these things that sound like fours, are fours, but you write them in compound time like 6/8 because it’s notationally easier. A true 6/8, or truly triple meter, is one where the movement of the tune coincides with the “6” in the top of the time signature. The exceptions – and they have to be learned – are the triple jig, the polonaise, and the sarabande, and very slow versions of either minuet or mazurka (and of course, many other styles of music that are not so commonly used in ballet).

To put it another way, what matters about time signature if you’re trying to make a bridge between movement and music is not how many beats there are in a bar, but whichbeats carry the motion. This rather 18th century way of looking at it helps to distinguish meter from subdivision. If you define time signature only as how many beats there are in a bar, without also looking in individual cases at what happens in the melody or most salient part of the musical surface, then meter and subdivision get confused. That’s the kind of class where hapless students try to count “12” in a bar of 12/8 where Koch would have said, “Don’t count 12, because this is mixed meter, it’s really a 4, written in 12 for the sake of notational simplicity.”

It’s rather a shame that I’ve only just realised this at the point in my life where I no longer have to teach it, but that’s why partly why I keep a blog – to atone for my past conceptual sins.

After 11 years of having odd articles about rhythm and metre all over my old site at jsmusic.org.uk, I decided it was time to reduce it all down to a page of the books and articles on rhythm that I got most of it from, rather than try to rewrite it to a standard that I’ll be happy with.

Although it might not seem like much, it’s a significant day in my life, and of my online life, because it signals the end of my belief that there is anything simple to say about meter and rhythm as soon as it gets outside of its comfort-zone of music notation for the purpose of reproducing music (mainly of the Western art music tradition). That’s not to say that you couldn’t teach the subject from an elementary entry point upwards – but what you’d start with would be very different to conventional music “theory” in the sense of time signatures and so on (I’d probably start with the tensions between time-discrete and time-continuous concepts of meter).

This variation by Mozart on “Ah, vous dirai-je maman”, K.265/300e has turned out to be a real life-saver in class for one of those ballet exercises where you need a 6/8 that gives you six quavers in a bar (click here to hear it). If you’re thinking “But that’s not a 6/8,” hold on, I’m coming to that, in this discussion of compound meter.

Ah, vous dirai-je maman’, K.265/300e, Variation 3

The Mozart is useful for class, but it’s also an example of a particular kind of 6/8 that does what you’d think it would do, i.e. articulate six quavers that you can hear and count. Not that you’d want to count them, but they’re there, so you can hear why it’s called a six. Many pieces in 6/8 don’t go like that (they just jig along rumpty-tumpty fashion, so they sound barely distinguishable from a 2, so to see why it’s a six, you have to imagine the beats that you can’t hear.

What is compound about compound meter?

It’s things like this that make me dread trying to explain compound meters such as 6/8, coupled with the fact that the term “compound meter” (or “compound time signature”) does not convey anything useful or hearable in the “compound” part. The meaning that “compound” once had in this context is rarely taught in music theory – that a 6/8 was at one time a way of writing two bars of 3/8 as compound bar, thus halving the number of barlines you had to draw.

Well, that’s part of the the story, at least. In Danuta Mirka’s Metric Manipulations in Haydn and Mozart, she explains that the eighteenth century theorist Koch viewed 6/8 sometimes as a “compound metre” in this sense, and sometimes as a “mixed meter” or a simple meter of “tripled beats”. That is, some 6/8s are basically just 2/4s with triplets (and some 9/8s are just 3/4s with triplets), but for notational ease, you might sometimes write the “tripled” 2/4 as 6/8.

The difference is crucial – one is triple subdivision (tripled 2/4), the other (compound 6/8) is triple meter, even if they’re both notated as 6/8. Which brings us back to a well-worn topic on this site, truly triple meter. It’s truly triple rather than sextuple, because to Koch, it’s a compound of two 3/8 bars (with equal weight in both halves of the bar, and quavers establishing the meter. That in turn is one reason perhaps why Mozart didn’t write this as 6/8. It’s clearly duple, rocking between stronger and weak beats in each bar.

Is compound meter really just about subdividing beats into three?

This is why it’s so hard to teach about compound time signature as a concept to those (like dance teachers) who are trying to understand how it relates to hearing music. To recap a previous post: If you look at many music primers, they’ll tell you that compound time signatures are where the beats are divided into three, and simple are where they are divided into two. Nothing about the term “compound” suggests “divided into three”, and if you’re looking at a time signature like 6/8, unlike the simple meters, there is no visible beat to be divided, it’s already been divided as part of the time signature. It makes no sense, unless you explain what I’ve explained above, which also explains what is simple about simple meters – not that the beat is divided into two, but that the bars are single units, not joined together as in compound signatures. But also, “compound time signature” only describes one concept of 6/8, and one which does not continue into the 19th century and beyond, where we describe it as if it were a duple metre with triple subdivision.

That is the why the Mozart piece is relatively unusual, and so useful. It is duple with triple subdivision, but it tips over into the realm of a truly triple meter because the movement that one hears, clearly on the musical surface, is of a continuous triple meter. It is hard to retain tripleness in the metrical slipstream of a piece which is duple at another level, but Mozart does it. Tears for Fears’ song “Everybody wants to rule the world” does it some of the time – there’s a constant, steady, truly triple 6/8 going on in a lot of the music, but the vocal line exerts a strong duple pull. Mozart’s advantage is that the tripleness is centre-stage in the melody, it’s not a support act. In “Everybody wants to rule the world”, it’s not exactly melody and accompaniment, they are simultaneous, equally salient layers of the music which both draw your attention (incidentally, the song’s time signature as published is notated in 12/8 with (4/4) in brackets).

6/8: two meters/time signatures masquerading as one

Disambiguating 6/8s into those which are characterised by triplet subdivision, and those which are truly triple meter seems to me to solve the problem, because it’s how people in the real world hear this music. You could argue that you should teach basic time signature before these more complex topics, but to my mind, teaching “compound time signature” by saying it “means” dividing a beat into 3, is oversimplifying the case to the point where it becomes difficult to understand because it doesn’t make sense. Koch’s theory isn’t simple, but it makes sense, and it reflects clearly the fact that 6/8 is not a single concept, but, echoing Justin London’s “many meters hypothesis”, it is a structure that has multiple expressions in real music. A differentiation between two types of 6/8 is partially clarified in Labanotation and Benesh Notation, because you have to say what level of the beat you’re using as your pulse. However, the issue here is not about the pulse that you count or sense as being the main beat, but level of beat where the musical action happens. Music could be truly sextuple (i.e. triple x 2) compositionally, but whereas a dancer might not count it that way if it’s fast, the composer on the other still writes it that way, because that’s how the music moves.

It would be good if in ballet teaching we had words to describe different kinds of 6/8, at least at the point at which you learn about time signatures, so that you can account for the fact that some don’t sound like six at all, and some do. We need something like a “triplety-two” and “truly sextuple” and a “swingy two” for those things like 6/8 marches that barely reveal any of their sixy undergarments, and possibly a few more. Dance rhythms are handy – but only if both parties (teacher and musician) have the same shared vocabulary and understanding, and only up to a point. It would be nice to be able to have something that was like a 6/8 march metrically, but wasn’t a 6/8 march culturally (or is that impossible?). Any ideas for some new terms?

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A blog about music, IT and dance some of the time, and eclectic personal trivia the rest of the time. I've moved here from www.jsmusic.org.uk, where the software was beginning to fall over, but don't worry, all the old stuff is still there if you're looking for it.
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